we are given
f(x)=[x=1]
where bracket means ceiling functions
we know that
Ceiling function returns the least value of the integer that is greater than or equal to the specified number
so, we can check each options
option-A:
At x=-4:
f(x)=[-4-1] =-5
For x<-3:
Let's assume
x=-3.1
f(x)=[-3.1-1] =[-4.1]=-5
so, this interval is TRUE
option-B:
At x=-2:
f(x)=[-2-1] =-3
For x<-1:
Let's assume
x=-1.1
f(x)=[-1.1-1] =[-2.1]=-3
so, this is FALSE
Answer:
Step-by-step explanation:
To write an equation into slope-intercept form, or y = mx + b format, we need to find the y-intercept of the line and its slope and substitute values for m and b.
1) First, find the y-intercept. The y-intercept is the point at which the line intersects the y-axis. Reading the graph, we can see that the line passes the y-axis at the point (0,2), thus that is the y-intercept.
2) Next, find the slope. Pick out two points on the graph to use for the slope formula, . I chose to work with (0,2) and (6,1). Now, substitute the two points' x and y values into the formula appropriately and solve:
Thus, is the slope.
3) Now, substitute the calculated values into the y = mx + b format. The b represents y-value of the y-intercept. The y-intercept is (0,2), thus substitute 2 for b. The coefficient of the x term, or m, represents the slope, thus substitute for m. This will give the following equation of the line in slope-intercept format: